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    <title>Fractal Rendering</title>
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          <h4 id="title">Fractal Rendering</h4>
          <div id="map" class="map"></div>
<label for="depth">
  depth:&nbsp;
  <input id="depth" type="range" min="0" max="9" step="1" value="5">
  &nbsp;(<span id="count">#</span> points)
</label>

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          <p id="shortdesc">Example of a fractal.</p>
          <div id="docs"><p>This example demonstrates how features with many vertices can be efficiently rendered.</p>
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          <div id="api-links">Related API documentation: <ul class="inline"><li><a href="../apidoc/ol.Feature.html" title="API documentation for ol.Feature">ol.Feature</a></li>,<li><a href="../apidoc/ol.Map.html" title="API documentation for ol.Map">ol.Map</a></li>,<li><a href="../apidoc/ol.View.html" title="API documentation for ol.View">ol.View</a></li>,<li><a href="../apidoc/ol.geom.LineString.html" title="API documentation for ol.geom.LineString">ol.geom.LineString</a></li>,<li><a href="../apidoc/ol.layer.Vector.html" title="API documentation for ol.layer.Vector">ol.layer.Vector</a></li>,<li><a href="../apidoc/ol.source.Vector.html" title="API documentation for ol.source.Vector">ol.source.Vector</a></li></ul></div>
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          <textarea class="hidden" name="title">Fractal Rendering</textarea>
          <textarea class="hidden" name="description">Example of a fractal.</textarea>
          <textarea class="hidden" name="js">var radius &#x3D; 10e6;
var cos30 &#x3D; Math.cos(Math.PI / 6);
var sin30 &#x3D; Math.sin(Math.PI / 6);
var rise &#x3D; radius * sin30;
var run &#x3D; radius * cos30;

var triangle &#x3D; new ol.geom.LineString([
  [0, radius], [run, -rise], [-run, -rise], [0, radius]
]);

var feature &#x3D; new ol.Feature(triangle);

var layer &#x3D; new ol.layer.Vector({
  source: new ol.source.Vector({
    features: [feature]
  })
});

var map &#x3D; new ol.Map({
  layers: [layer],
  target: &#x27;map&#x27;,
  view: new ol.View({
    center: [0, 0],
    zoom: 1
  })
});

function makeFractal(depth) {
  var geometry &#x3D; triangle.clone();
  var graph &#x3D; coordsToGraph(geometry.getCoordinates());
  for (var i &#x3D; 0; i &lt; depth; ++i) {
    var node &#x3D; graph;
    while (node.next) {
      var next &#x3D; node.next;
      injectNodes(node);
      node &#x3D; next;
    }
  }
  var coordinates &#x3D; graphToCoords(graph);
  document.getElementById(&#x27;count&#x27;).innerHTML &#x3D; coordinates.length;
  geometry.setCoordinates(coordinates);
  feature.setGeometry(geometry);
}

function injectNodes(startNode) {
  var endNode &#x3D; startNode.next;

  var start &#x3D; startNode.point;
  var end &#x3D; startNode.next.point;
  var dx &#x3D; end[0] - start[0];
  var dy &#x3D; end[1] - start[1];

  // first point at 1/3 along the segment
  var firstNode &#x3D; {
    point: [start[0] + dx / 3, start[1] + dy / 3]
  };

  // second point at peak of _/\_
  var r &#x3D; Math.sqrt(dx * dx + dy * dy) / (2 * cos30);
  var a &#x3D; Math.atan2(dy, dx) + Math.PI / 6;
  var secondNode &#x3D; {
    point: [start[0] + r * Math.cos(a), start[1] + r * Math.sin(a)]
  };

  // third point at 2/3 along the segment
  var thirdNode &#x3D; {
    point: [end[0] - dx / 3, end[1] - dy / 3]
  };

  startNode.next &#x3D; firstNode;
  firstNode.next &#x3D; secondNode;
  secondNode.next &#x3D; thirdNode;
  thirdNode.next &#x3D; endNode;
}


function coordsToGraph(coordinates) {
  var graph &#x3D; {
    point: coordinates[0]
  };
  var length &#x3D; coordinates.length;
  for (var level &#x3D; 0, node &#x3D; graph; level &lt; length - 1; ++level) {
    node.next &#x3D; {
      point: coordinates[level + 1]
    };
    node &#x3D; node.next;
  }
  return graph;
}

function graphToCoords(graph) {
  var coordinates &#x3D; [graph.point];
  for (var node &#x3D; graph, i &#x3D; 1; node.next; node &#x3D; node.next, ++i) {
    coordinates[i] &#x3D; node.next.point;
  }
  return coordinates;
}

var depthInput &#x3D; document.getElementById(&#x27;depth&#x27;);

function update() {
  makeFractal(Number(depthInput.value));
}

var updateTimer;


/**
 * Regenerate fractal on depth change.  Change events are debounced so updates
 * only occur every 200ms.
 */
depthInput.onchange &#x3D; function() {
  window.clearTimeout(updateTimer);
  updateTimer &#x3D; window.setTimeout(update, 200);
};

update();
</textarea>
          <textarea class="hidden" name="css">.map {
  background: whitesmoke;
}
#depth {
  width: 100px;
}
</textarea>
          <textarea class="hidden" name="html">&lt;div id&#x3D;&quot;map&quot; class&#x3D;&quot;map&quot;&gt;&lt;/div&gt;
&lt;label for&#x3D;&quot;depth&quot;&gt;
  depth:&amp;nbsp;
  &lt;input id&#x3D;&quot;depth&quot; type&#x3D;&quot;range&quot; min&#x3D;&quot;0&quot; max&#x3D;&quot;9&quot; step&#x3D;&quot;1&quot; value&#x3D;&quot;5&quot;&gt;
  &amp;nbsp;(&lt;span id&#x3D;&quot;count&quot;&gt;#&lt;/span&gt; points)
&lt;/label&gt;
</textarea>
          <input type="hidden" name="resources" value="https://openlayers.org/en/v4.4.2/css/ol.css,https://openlayers.org/en/v4.4.2/build/ol.js">
          <input type="hidden" name="data">
        </form>
        <pre><code id="example-source" class="language-markup">&lt;!DOCTYPE html&gt;
&lt;html&gt;
  &lt;head&gt;
    &lt;title&gt;Fractal Rendering&lt;/title&gt;
    &lt;link rel="stylesheet" href="https://openlayers.org/en/v4.4.2/css/ol.css" type="text/css"&gt;
    &lt;!-- The line below is only needed for old environments like Internet Explorer and Android 4.x --&gt;
    &lt;script src="https://cdn.polyfill.io/v2/polyfill.min.js?features=requestAnimationFrame,Element.prototype.classList,URL"&gt;&lt;/script&gt;
    &lt;script src="https://openlayers.org/en/v4.4.2/build/ol.js"&gt;&lt;/script&gt;
    &lt;style&gt;
      .map {
        background: whitesmoke;
      }
      #depth {
        width: 100px;
      }
    &lt;/style&gt;
  &lt;/head&gt;
  &lt;body&gt;
    &lt;div id&#x3D;&quot;map&quot; class&#x3D;&quot;map&quot;&gt;&lt;/div&gt;
    &lt;label for&#x3D;&quot;depth&quot;&gt;
      depth:&amp;nbsp;
      &lt;input id&#x3D;&quot;depth&quot; type&#x3D;&quot;range&quot; min&#x3D;&quot;0&quot; max&#x3D;&quot;9&quot; step&#x3D;&quot;1&quot; value&#x3D;&quot;5&quot;&gt;
      &amp;nbsp;(&lt;span id&#x3D;&quot;count&quot;&gt;#&lt;/span&gt; points)
    &lt;/label&gt;
    &lt;script&gt;
      var radius &#x3D; 10e6;
      var cos30 &#x3D; Math.cos(Math.PI / 6);
      var sin30 &#x3D; Math.sin(Math.PI / 6);
      var rise &#x3D; radius * sin30;
      var run &#x3D; radius * cos30;

      var triangle &#x3D; new ol.geom.LineString([
        [0, radius], [run, -rise], [-run, -rise], [0, radius]
      ]);

      var feature &#x3D; new ol.Feature(triangle);

      var layer &#x3D; new ol.layer.Vector({
        source: new ol.source.Vector({
          features: [feature]
        })
      });

      var map &#x3D; new ol.Map({
        layers: [layer],
        target: &#x27;map&#x27;,
        view: new ol.View({
          center: [0, 0],
          zoom: 1
        })
      });

      function makeFractal(depth) {
        var geometry &#x3D; triangle.clone();
        var graph &#x3D; coordsToGraph(geometry.getCoordinates());
        for (var i &#x3D; 0; i &lt; depth; ++i) {
          var node &#x3D; graph;
          while (node.next) {
            var next &#x3D; node.next;
            injectNodes(node);
            node &#x3D; next;
          }
        }
        var coordinates &#x3D; graphToCoords(graph);
        document.getElementById(&#x27;count&#x27;).innerHTML &#x3D; coordinates.length;
        geometry.setCoordinates(coordinates);
        feature.setGeometry(geometry);
      }

      function injectNodes(startNode) {
        var endNode &#x3D; startNode.next;

        var start &#x3D; startNode.point;
        var end &#x3D; startNode.next.point;
        var dx &#x3D; end[0] - start[0];
        var dy &#x3D; end[1] - start[1];

        // first point at 1/3 along the segment
        var firstNode &#x3D; {
          point: [start[0] + dx / 3, start[1] + dy / 3]
        };

        // second point at peak of _/\_
        var r &#x3D; Math.sqrt(dx * dx + dy * dy) / (2 * cos30);
        var a &#x3D; Math.atan2(dy, dx) + Math.PI / 6;
        var secondNode &#x3D; {
          point: [start[0] + r * Math.cos(a), start[1] + r * Math.sin(a)]
        };

        // third point at 2/3 along the segment
        var thirdNode &#x3D; {
          point: [end[0] - dx / 3, end[1] - dy / 3]
        };

        startNode.next &#x3D; firstNode;
        firstNode.next &#x3D; secondNode;
        secondNode.next &#x3D; thirdNode;
        thirdNode.next &#x3D; endNode;
      }


      function coordsToGraph(coordinates) {
        var graph &#x3D; {
          point: coordinates[0]
        };
        var length &#x3D; coordinates.length;
        for (var level &#x3D; 0, node &#x3D; graph; level &lt; length - 1; ++level) {
          node.next &#x3D; {
            point: coordinates[level + 1]
          };
          node &#x3D; node.next;
        }
        return graph;
      }

      function graphToCoords(graph) {
        var coordinates &#x3D; [graph.point];
        for (var node &#x3D; graph, i &#x3D; 1; node.next; node &#x3D; node.next, ++i) {
          coordinates[i] &#x3D; node.next.point;
        }
        return coordinates;
      }

      var depthInput &#x3D; document.getElementById(&#x27;depth&#x27;);

      function update() {
        makeFractal(Number(depthInput.value));
      }

      var updateTimer;


      /**
       * Regenerate fractal on depth change.  Change events are debounced so updates
       * only occur every 200ms.
       */
      depthInput.onchange &#x3D; function() {
        window.clearTimeout(updateTimer);
        updateTimer &#x3D; window.setTimeout(update, 200);
      };

      update();
    &lt;/script&gt;
  &lt;/body&gt;
&lt;/html&gt;</code></pre>
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